Getting the residence card with no postal address.

Hi
          First you have to change your address on skatt.no ( tax.no)  This usually takes about 5 working days to have it processed by the tax authorities.  Writing your name on mail box of Airbnb temporal residence does not make any difference without the internet change of address. so my advice is to keep your address where you have been living until you receive your residence card. alternatively,  you can contact Posten they can instantly make it possible to direct your post letter to the place your want them to do before your address change is process by the tax authorities. Note that there is a fee for this about 250/300kr.
Hope this helps

just a little information.  I have not done it myself but a friend told me about it.  he only told me it works when it comes to picking up the card from UDI.

Once your application is approved, you will be asked to go to UDI to take biometric and photo for the card.  during that appointment, you can tell the officer that you wish to pick up the card DIRECTLY from the UDI office.  Then they will let you know the time and date to pick up the card, instead of the card being sent to the address.

this is useful because some of the post office counters in norway will insist on seeing some credentials before releasing the card.  They don't trust passports etc.  They only trust driving licenses or bank card with photo id.   A lot of banks stop issuing bank card with photo to foreigners and not everyone drives.  At least UDI still recognize passports as identification document.